| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Outline of Final Research Achievements |
The Riemann-Hilbert correspondence assigns a linear differential equation whose solution space is finite dimensional to the solution space with derived topological data. Concretely, derived topological data described by homology cycles or de Rham cohomology classes. In fact, de Rham cohomology classes are represented by differential forms and homology cycles play rolls as integration paths. The integrals of thoseforms along those paths define special functions as the hypergeometric functions. That correspondence gives a categorical equivalence. In our research, we discover a parallel story in the world of q-analysis.
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